Question

11 multiple choice 1 point
a spring (k = 790 n/m) has a length of 48 cm when zero net force is applied to it. what will its length be when 230 n of force is applied to stretch it?
0.77 m
3.4 m
3.9 m
0.29 m

Explanation:

Step1: Use Hooke's Law

Hooke's Law is \(F = kx\), where \(F\) is the force, \(k\) is the spring constant, and \(x\) is the extension. We need to find \(x\). Rearranging for \(x\) gives \(x=\frac{F}{k}\).
Substitute \(F = 230\space N\) and \(k=790\space N/m\) into the formula: \(x=\frac{230}{790}\space m\approx0.291\space m\).

Step2: Calculate the new length

The original length \(L_0 = 48\space cm=0.48\space m\). The new length \(L = L_0 + x\).
Substitute \(L_0 = 0.48\space m\) and \(x\approx0.291\space m\) into the formula: \(L=0.48 + 0.291=0.771\space m\approx0.77\space m\).

Answer:

0.77 m